Question: $ C = \left[\begin{array}{rrr}-2 & 1 & 4 \\ 0 & 2 & 0 \\ -2 & -1 & 1\end{array}\right]$ $ B = \left[\begin{array}{r}1 \\ -1 \\ -2\end{array}\right]$ Is $ C- B$ defined?
Solution: In order for subtraction of two matrices to be defined, the matrices must have the same dimensions. If $ C$ is of dimension $( m \times  n)$ and $ B$ is of dimension $( p \times  q)$ , then for their difference to be defined: 1. $ m$ (number of rows in $ C$ ) must equal $ p$ (number of rows in $ B$ ) and 2. $ n$ (number of columns in $ C$ ) must equal $ q$ (number of columns in $ B$ Do $ C$ and $ B$ have the same number of rows? Yes Yes No Yes Do $ C$ and $ B$ have the same number of columns? No Yes No No Since $ C$ has different dimensions $(3\times3)$ from $ B$ $(3\times1)$, $ C- B$ is not defined.